Direct CP Violation in B decays with rho0-omega Mixing

A complete study of the process B to pi+ pi- V(V=1--) is performed both in the framework of the helicity formalism and the effective lagrangian approach. Emphasis is put on the factorization hypothesis and the importance of the rho0- omega mixing in enhancing the direct CP violation. New results involving some branching ratios and the ratio of the Penguin/Tree amplitude are given in details.